30
2 Zero-Index Metamaterials
get violated if phase velocity becomes greater than c, or even infinite, as it has no
physical significance. The group velocity is the actual rate of transfer of energy,
which is always less than c, according to Eq. 2.5. Hence, zero refractive index is a
very natural property of certain physical systems.
2.4 Zero-Index Metamaterials
2.4.1 Basic Idea
Any medium whose effective refractive index varies from negative to positive range is
bound to exhibit zero refractive index at the frequency of transition, i.e., the frequency
at which the refractive index curve intersects the x-axis. This type of dispersion is
abnormal for natural materials but plausible for metamaterials. For example, let us
consider the well-acknowledged fishnet-type negative-index metamaterial. A fishnet
metamaterial consists of a dielectric layer sandwiched between two metal layers and
each layer has the same patterning throughout [31, 32, 104]. A typical unit cell of a
fishnet metamaterial is shown in Fig. 2.3a and its effective refractive index is shown in
Fig. 2.3b. The effective refractive index has been calculated from s-parameters using
retrieval technique of Smith et al. [19], according to which the effective material
parameters, i.e., the refractive index (n), the impedance (z), the permittivity (), and
the permeability (μ) are calculated as follows:
n =
1
kd
cos
−1
1
2S 21
(1 − S
2
11 + S
2
21 )
(2.6)
z =
(1 + S 11 ) 2 − S
2
21
(1 − S 11 ) 2 − S
2
21
,
(2.7)
= n/z,
(2.8)
μ = nz
(2.9)
It can be seen in Fig. 2.3b that as the wavelength increases, the refractive index
transits from positive to negative values, continues to remain negative for a range
of wavelengths, and then returns to the positive domain. The two points of transition, corresponding to 1530 nm and 1630 nm, are the points of zero refractive index
behavior. Investigation of optical properties at these two wavelengths can pave the
way for several interesting applications. However, being a metallic structure, a fishnet metamaterial has huge ohmic loss, rendering it a poor choice as a zero-index
metamaterial.
2 Zero-Index Metamaterials
get violated if phase velocity becomes greater than c, or even infinite, as it has no
physical significance. The group velocity is the actual rate of transfer of energy,
which is always less than c, according to Eq. 2.5. Hence, zero refractive index is a
very natural property of certain physical systems.
2.4 Zero-Index Metamaterials
2.4.1 Basic Idea
Any medium whose effective refractive index varies from negative to positive range is
bound to exhibit zero refractive index at the frequency of transition, i.e., the frequency
at which the refractive index curve intersects the x-axis. This type of dispersion is
abnormal for natural materials but plausible for metamaterials. For example, let us
consider the well-acknowledged fishnet-type negative-index metamaterial. A fishnet
metamaterial consists of a dielectric layer sandwiched between two metal layers and
each layer has the same patterning throughout [31, 32, 104]. A typical unit cell of a
fishnet metamaterial is shown in Fig. 2.3a and its effective refractive index is shown in
Fig. 2.3b. The effective refractive index has been calculated from s-parameters using
retrieval technique of Smith et al. [19], according to which the effective material
parameters, i.e., the refractive index (n), the impedance (z), the permittivity (), and
the permeability (μ) are calculated as follows:
n =
1
kd
cos
−1
1
2S 21
(1 − S
2
11 + S
2
21 )
(2.6)
z =
(1 + S 11 ) 2 − S
2
21
(1 − S 11 ) 2 − S
2
21
,
(2.7)
= n/z,
(2.8)
μ = nz
(2.9)
It can be seen in Fig. 2.3b that as the wavelength increases, the refractive index
transits from positive to negative values, continues to remain negative for a range
of wavelengths, and then returns to the positive domain. The two points of transition, corresponding to 1530 nm and 1630 nm, are the points of zero refractive index
behavior. Investigation of optical properties at these two wavelengths can pave the
way for several interesting applications. However, being a metallic structure, a fishnet metamaterial has huge ohmic loss, rendering it a poor choice as a zero-index
metamaterial.